Question about using a fish tape for coax runs

My old boss in Phoenix always said to never use a metal fish tape on existing coax lines, but a new guy on my crew swears by it for tricky pulls. Last job, we tried his way and ended up nicking the sheathing on a line in the wall. Who's right here, and what's your go-to method?

I used to think the moon landing was fake, but my brother's friend who works at JPL said something that got me.